An arrangement in which, when a transmission is connected via a torque converter to an engine that can run in a cylinder cut-off state, in order to prevent torque variation at the time of switching over between cylinder cut-off running and all-cylinder running of the engine from being transmitted as a shock to the vehicle body, the slip ratio of the lock-up clutch of the torque converter is temporarily increased at the time of switching, is known from Patent Document 1 below.